Theorems · Theorem · functional analysis
ClosedSubmodule.inf_orthogonal_eq_bot
∀ {𝕜 : Type u_4} {E : Type u_5} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
(K : ClosedSubmodule 𝕜 E), K ⊓ Kᗮ = ⊥K and Kᗮ have trivial intersection.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 183 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NormedAddCommGroupstatement and proof · cited by 15,752
- Bot.botstatement · cited by 4,720
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- Inner.innerproof · cited by 1,089
- eq_bot_iffproof · cited by 159
- ClosedSubmodulestatement and proof · cited by 123
- ClosedSubmodule.orthogonalstatement · cited by 32
- inner_self_eq_zeroproof · cited by 18
Cited by1
Results whose statement or proof uses this declaration.
- ClosedSubmodule.orthogonal_disjointproof · cited by 1